SignalUtils::DcFilter Function

Design a DC filter.

Design a DC filter with TransitionBandwidth and place the transfer function in Num (numerator) and Den (denominator). You can then use this transfer function to initialize an IIR filter with a call to IirInit.

A DC filtered signal will be centered around zero. This DC filter is a simple differentiator/integrator pair. Transition bandwidth is the width of the frequency band where the amplitude is not yet completely attenuated. With DC filters, the transition band starts at 0 Hz. Narrow transition band (TransitionBandwidth/FS ratio is small) will result in filters with longer delays. FS is the sampling frequency. The filter implements the following difference equation:

y[i] = x[i] - x[i-1] + alpha y[i-1]

x.. input signal
y.. output signal
alpha.. parameter

Alpha paremeter can control the 3dB frequency of the transition bandwidth:

alpha := 1-(TransitionBandwidth/FS)*Pi;

FS.. sampling frequency
TransitionBandwidth.. frequency up to which will the filter have more
                      then 3dB attenuation. Must be less then FS/2.

Design a DC-blocking (high-pass) IIR filter from alpha.

Builds the transfer function of a first-order DC blocker and stores it in num / den for use with IirInit / IirFilter; the filtered signal is centred around zero (its mean is removed). With unity-DC-gain correction g = alpha/big(alpha + 1/2(1-alpha)big) the filter is

H(z) = g (1 - z^(-1))/(1 - alpha z^(-1))

i.e. a differentiator/integrator pair with a zero at z=1 (DC) and a pole at z=alpha. Domain: 0 < alpha < 1 (typically 0.99-0.9999); alpha nearer 1 pushes the cut-off lower and lengthens the transient. A finite alpha in range yields finite coefficients.

State parameter holds the filter state.

NewValue is the next sample and alpha is typically between 0.99 and 0.9999 and must be < 1. Big alpha will cause longer filter delay and more ringing. State should be initialized to zero before the routine is called for the first time.